Project ForgeEngineering Mathematics
Calculus
GATE 2018
Medium
An explicit forward Euler method is used to numerically integrate the differential equation dy/dt = y using a time step of 0.1. With the initial condition y(0)=1, the value of y(1) computed by this method is __________ (correct to two decimal places).
2.6(± 0.05 accepted)
Explanation
Forward Euler: y_{n+1} = y_n + h·y_n = y_n(1+h) = 1.1·y_n. Reaching t=1 from t=0 with h=0.1 takes 10 steps: y(1) = y(0)×1.1¹⁰ = 1×2.5937 ≈ 2.59.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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